In the field of communications and signal processing, it is well known that an original sampling rate for sampling a signal must satisfy the sampling theorem, which states that the signal to be digitized is band-limited and has an upper cutoff frequency which is less than half the sampling rate. To obtain a sampling-rate increase or reduction by arbitrary factors, filter combinations have proved to be effective, which are also referred to as "hybrid systems". The basic idea is that the low-pass-filtered input data sequence is converted into an analog signal which is then digitized again at the desired sampling rate. In intermediate stages, of course, digital and analog low-pass filtering is performed whose cutoff frequencies are matched to the respective internal and external sampling rates and signal frequencies, so that no aliasing will occur in the output data sequence.
Reconstructing an analog signal within the filter combination by digital-to-analog conversion is possible in principle, but this approach serves mainly to explain the method. For the actual implementation, complete reconstruction of the analog signal is not necessary, since the desired intermediate values can be calculated with a high degree of accuracy by all-digital means via an interpolation of the digital samples. Conversion into an analog signal would be an unnecessary and roundabout way, since for sampling rate conversion, only a single intermediate value between fixed, given values has to be interpolated for each new sample. The analog signal waveform on both sides of this interpolated intermediate value is not needed for the output data sequence. The given values may be actual and/or interpolated samples; in any case, they are defined by a fixed sampling sequence. Therefore, the filter which provides the given values is also referred to as a fixed or time-invariant interpolation filter. As a rule, the frequency of this new sampling sequence is higher than the original sampling frequency by a power of two. Such filter combinations are exhaustively described, for example, in an article by T. A. Ramstad, "Digital Methods for Conversion Between Arbitrary Sampling Frequencies", IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. ASSP-32, No. 3, June 1984.
Co-pending, commonly assigned U.S. patent application Ser. No. 08/984735 entitled "DIGITAL FILTER COMBINATION FOR INTERPOLATION" filed on Dec. 3, 1997 and incorporated herein by reference discloses a digital filter combination for interpolating samples of a digitized signal whereby the sampling rate of digitized video or audio signals can be changed by an arbitrary numerical ratio. The circuit includes a third-order time-invariant interpolation filter with which the number of existing samples is doubled by forming interpolated intermediate values. Two samples are assigned to one period of the original sampling clock. For the further processing, this is tantamount to a doubling of the original sampling rate, since the available samples now correspond to a sampling sequence with one-half the original period. The time-invariant interpolation filter is followed by a second-order time-varying interpolation filter which can calculate intermediate values from the new sampling sequence for the desired output sequence for any points of time.
If the sampling rates at the input and output ends are similar to each other, the filter complexity will remain within reasonable limits. Things are different if the two sampling rates differ widely, because the mirroring of the existing signal spectrum at the new sampling rate and the associated frequency multiples may result in aliasing. The suppression of these frequency components in the signal spectrum, which is generally carried out prior to the sampling rate conversion, requires complex low-pass filters, such as transversal filters with long delay cascades. The band limiting becomes even more complex if the bandwidth must be adjustable in several steps because the sampling-rate ratio must be arbitrarily adjustable within given limits. The band limiting may thus become much more complex than the sampling rate conversion proper. For consumer applications, the complexity involved in implementing a particular function is an important quantity: the higher the circuit complexity, the greater the amount of semiconductor area required for this function during monolithic integration. As is well known, the increased semiconductor area requirement enters disproportionately into the manufacturing costs.
It is therefore an object of the invention to keep the overall circuit complexity for arbitrary sampling rate conversion to a minimum.